The purpose of this paper is to demonstrate that it is possible to communicate over a memoryless channel of capacity

at any rate

with a probability of error less than

, per block of a length approximately proportional to

and with a computational decoding complexity which is asymptotically proportional to

when

is large. The decoding scheme presented in this paper is based on a two-cycle iteration of a decoding procedure which has been described in an earlier paper [1 ].